How to Calculate g with Known Pendulum Length and Negligible Amplitude?

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SUMMARY

The calculation of gravitational acceleration (g) using a simple pendulum involves the formula T=2π√(L/g), where T is the period and L is the length of the pendulum. To isolate g, rearranging the formula yields g = (4π²L)/(T²). The discussion emphasizes that the length of the pendulum does not inherently depend on the strength of gravity, as 1 meter remains 1 meter regardless of the gravitational field, such as on Jupiter or the Moon. The key takeaway is the relationship between the period of the pendulum and gravitational acceleration, which is crucial for accurate calculations.

PREREQUISITES
  • Understanding of simple harmonic motion
  • Familiarity with the formula for the period of a pendulum
  • Basic algebra for rearranging equations
  • Knowledge of gravitational acceleration concepts
NEXT STEPS
  • Research the derivation of the pendulum period formula
  • Explore the effects of varying gravitational fields on pendulum motion
  • Learn about the impact of amplitude on pendulum calculations
  • Investigate experimental methods for measuring g using pendulums
USEFUL FOR

Physics students, educators, and anyone interested in understanding the principles of pendulum motion and gravitational calculations.

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How to calculate g if amplitude of a simple pendulum is negligible and the length is known?




T=2π\sqrt{}l/g
 
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In terms of the period? Just solve for g in terms of T and L.
 
No, only in terms of L.
 
Check your problem:
Why should the length L depend on the strength of gravity? This is usually something you just cut to whatever length you like - 1m on Jupiter is the same as 1m on the moon... unless, I suppose, you are doing the measuring from a different gravity from the one the meter is in? (This forum I don't want to make too many assumptions!)
 

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